JOURNAL OF LUMINESCENCE 1,2 (1970) 693-701
© North-Holland Publishing Co., Amsterdam
INFLUENCE OF A DIELECTRIC INTERFACE
ON FLUORESCENCE DECAY TIME
K. H. DREXHAGE*
IBM Research Laboratory, San Jose, California, USA
When a mirror is placed near a fluorescing molecule, not only the angular distribution
of the fluorescence is affected, but also the decay time. This effect is considered for the
case of the reflecting interface between two dielectrics of different refractive indices. The
fluorescence decay time varies markedly due to the presence of such an interface. In case
of fluorescing molecules placed directly at the interface between a medium of refractive
index 1.54 and air, the decay time is lengthened by a factor of 1.08 if their transition
moment is oriented parallel to the interface, and by a factor of 3.61 if the transition
moment is oriented perpendicular to the interface. These considerations are compared
with measurements on monomolecular layers of an europium dibenzoylmethane complex
which were held at a variable, but well defined distance from the interface.
if one places an excited molecule (or atom) in front of a mirror, then the
emission of radiation (fluorescence, phosphorescence) is influenced by the
mirror. This comes about because part ofthe emitted light wave is reflected by
the mirror and interferes with the non-reflected part. Let us consider the
radiation of an oscillating electric dipole, which is emitted at a certain
angle to the mirror normal (fig. I, left). There the path difference between
the direct and reflected beam is such that constructive interference occurs and
therefore the molecule will radiate strongly in this direction. However, at a
somewhat larger angle (fig. 1, right) the path difference is half a wavelength
smaller so that the direct and reflected beam interfere destructively. If the
reflectivity of the mirror equals lOO~,the amplitude of the reflected wave
is as large as the amplitude of the direct wave and therefore both cancel
in this particular direction. The molecule will not radiate in this direction
at all.
The angular distribution P(O) of the fluorescence intensity, polarized
perpendicular to the plane of incidence on the mirror is given’ _3) by:
ö
P(O) = I + p~(O)+ 2p~(O)cos [(4mnd/2) cos 0
1(0)],
(I)
—
0
d
=
*
Present address: Eastman Kodak Research Laboratories, Rochester, New York, USA.
=
angle between the direction of light emission and mirror normal;
distance between excited molecule and mirror; n = refractive index of
693
1.2
694
1.2
K. H. DREXHAGE
Amplification
by Interference
Quenching
by Interference
/1
V\\\\\\\\\‘~
___
~N~~\\~\\\\
~\\\\~N’~\
Mirror
Fig. I. Electric dipole radiation interacting with plane mirror.
the medium in front of the mirror; ). = vacuum wave length of the emitted
light.
The reflection coefficient p~and the phase shift O1 are in general dependent
on the angle of incidence 0 and can be calculated from Fresnel’s formulae.
As is seen from eq. (I) the fluorescence intensity in front of the mirror should
exhibit a pattern well known from the emission of radio waves by antennas.
The larger the distance d the more maxima and minima will occur.
We have investigated this effect on a europium-dibenzoylmethane complex, the
of which
placed absorb
at a wellstrongly
definedindistance
froni the
3). molecules
The ligands
of thiswere
complex
the ultraviolet.
mirror
After intramolecular energy transfer to the central Eu3~-ionthis fluoresces
with high quantum yield at about 612 nm. Fig. 2 shows the fluorescence of
this compound placed at a distance of 6770 A from a gold mirror. The
measured angular distribution (full line) agrees very well with the calculation
according to eq. (I) (dashed line).
O~234
90’
Fig. 2. Angular distribution of fluorescence of eLlropium-dibenzoylmcthane complex
6770 A from gold mirror.
1.2
695
INFLUENCE OF A DIELECTRIC INTERFACE ON FLUORESCENCE DECAY TIME
The mirror not only influences the angular distribution of the fluorescence
intensity, but also the fluorescence decay time. To understand this effect
let us consider an excited molecule in the very center of a spherical mirror
(fig. 3). If the radius of the mirror is for instance 1.75 (fig. 3, upper case),
,~
Amplification by interference:
dipole radiates twice the power
as without the mirror (TM=~t)
/1
/
Radius 1.75X
Quenching by interference:
dipole cannot radiate (TM=)
~L)
Radius 2X
Fig. 3. Radiation from excited molecule in center of spherical mirror.
constructive interference of the direct and reflected beam will occur in all
directions of the upper halfspace. Since the radiated intensity is proportional
to the square of the amplitude, the probability for radiation is four times as
large as without the mirror. Into the lower half space there is no radiation
due to the mirror. Therefore the integrated probability for radiation will be
twice as large as without the mirror. This means the decay time of the molecule
in the center of the mirror will be half the decay time of the molecule in free
space (assuming there are no competing radiationless deactivation processes).
On the other hand, if the radius of the spherical mirror is for instance 2A
(fig. 3, lower case), the direct and reflected beam interfere destructively and
thus the excited molecule cannot radiate at all. Under the same assumptions
as above it will stay high forever (decay time infinite).
In the same way as shown for a spherical mirror the fluorescence decay
time is affected by a plane mirror. We again integrate the intensity above
the mirror and find for the decay time ~ of an excited molecule1):
a. axis of electric dipole oscillator perpendicular to the mirror
=
[i
—
J
2) cos (xu
p
11(u) (1
—
u
—
oll(u))du]
;
(2)
696
1.2
K. H. DREXHAGE
b. axis of electric dipole oscillator parallel to the mirror
=
[I + ~ ~ p11(u)u2 cos (xu
—
+ ~
=
4rrnd/i,; u
=
J
p
1(u) cos (xu
—
b~(u))du
(3)
.
cos 0: P11(a), p1(u) reflection coefficients of the mirror,
~11(u), à1(u) phaseshifts on reflection by the mirror.
In the case of an idealized mirror with
p1
I and
ir.
independent of angle 0, the integrals in eqs. (2) and (3) can be easily solved
and one gets:
Case a.
1— 3cosx
2
+ 3sinxi
3
I1 ;
(4)
r.
=
=
=
=
~
X
-
j
X
Case b.
-
-
I— 3 sin x
2x
—
3 cos x
+
3 sin x1
2x2
1
.
(5)
2x3
However, in all practical cases the reflection coefficients and phaseshifts
depend in a complicated manner on the angle of incidence and on the
polarization of the light.
We have measured the influence of a mirror on the fluorescence decay
time for the first time using the above mentioned europium complex whose
fluorescence decay time is roughly I msec I)~ The environment of the emitting
Eu3~-ioncan be considered isotropic. Thus neither one of the particular
orientations considered above is applicable to this case. The probability
of light emission is rather foLind by averaging over the probability of case a.
plus twice the probability of case b. In this way the fluorescence decay time
in front of a silver mirror was calculated (fig. 4, full line). As can be seen
from this figure the fluorescence decay time should be lengthened or shortened
dependent on the distance d from the mirror.
In the above consideration we omitted possible radiationless deactivation
processes, which are not affected by the mirror. If we take them into account,
we find for the true decay time t’~
(6)
T’,
where
ij~, is
the
quantum
I +
ij~,, (i~ /t~
—
I)
yield of the emitting state, which we mtist carefully
1.2
INFLUENCE OF A DIELECTRIC INTERFACE ON FLUORESCENCE DECAY TIME
0
.0
Li
5
3~in front of silver mirror.
697
.a~i.
Fig. 4. Fluorescent decay time of Eu
distinguish from the quantum yield c~defined as the ratio between the
amounts of emitted and absorbed quanta. A quantum yield i~ < 1 leads
to a less pronounced variation of the fluorescence decay time in front of
the mirror, because in this case the radiationless deactivation processes
which are not affected by the mirror, have an influence on the decay time.
This is shown in fig. 4 for a quantum yield i~
0.7 (dashed line).
By comparing the curves t~/i~, calculated with different values i~, with
the experimental data one is able to determine directly the quantum yield
of the emitting state ij~, an otherwise hardly accessible quantity. In case
of the europium complex it was found: ,j~ 0.7 (fig. 5). The experimental
values of t~, measured by varying the distance d stepwise 52.8 A 1), agree
very well with the theory outlined above. The disagreement at very small
distances is due to energy transfer from the excited molecules to the silver
mirror, which shall not be considered here.
As the mirror influences selectively the light emission, but not the competing
radiationless deactivation processes, the quantum yield ,j~varies with the
distance from the mirror too. It follows quantitatively:
=
=
=
[I +
.i~(~L
—
—1•
(7)
698
1.2
K. H. DREXHAGE
3.
—
Theory (‘~0.7)
Experiment
P
0.5
1.0
[.5
2 in front of siker
Fig. 5. Comparison of theory and experiment
mirror.for decay time of Eu
Whereas a silver mirror has a high reflectivity at all angles of incidence, the
reflectivity of the interface between two media with different refractive index
varies strongly with the angle of incidence 0, being very high only at large
angles 0. However, by substituting the reflection coefficients and phase
shifts of such an interface into eqs. (2) and (3) a pronounced influence on the
fluorescence decay time is expected (fig. 6). Particularly in case of an electric
dipole oscillator whose axis is oriented perpendicular to the interface the
decay time is lengthened remarkably. If the ratio of the refractive indices
is for instance 1.54, the decay time of an excited molecule near the interface
will be lengthened by a factor of 3.61. If the ratio of the refractive indices
is 2.00. the lengthening factor amounts to a value as large as 9.31.
The considered phenomenon is dependent on the nature of the fluorescent
transition. The influence of a dielectric interface on a magnetic dipole
oscillator is shown in fig. 7. It turns out that in this case the decay time near
the mirror is also lengthened.
Experimental data on the europium complex are in fair agreement with
the expected curve which was calculated using the value ij~ 0.7 and taking
the average described above (fig. 8).
Finally, we want to mention that a reflector will affect the probability
=
1.2
INFLUENCE
699
OF A DIELECTRIC INTERFACE ON FLUORESCENCE DECAY TIME
O~5O
.5
Fig. 6. Decay time of electric dipole oscillator in front of a dielectric interface.
7;
3
n,0.54
2
n
2=l.00
‘I’—
n. d
0
0.5
1.0
1.5
X
Fig. 7. Decay time of magnetic dipole oscillator in front of a dielectric interface.
700
1.2
K. H. DREXUAGF
3.
.54
n
2~l.00
Theory (~:Q7)
2
-
0
~-
0.5
[.0
Experiment
.5
2 in front of a dielectric interface.
Fig. 8. Fluorescent decay time of Eu
of any emission process. It has long been known that the impedance of a
radio antenna is changed by a reflector. In this paper it is shown that the
probability of light emission is influenced by a mirror, which may be merely
a dielectric interface. If we are allowed to extend our considerations to even
shorter wavelengths, i.e. the emission of y-quanta by nuclei, an interesting
conclusion can be drawn: if we had a mirror for y-rays. we would be able to
influence the lifetime of radio-active nuclei.
References
I) K. H. Drexhagc, Optische Lintersuchungen an neuartigen monomolekularen Farhstoffschichten (Habilitations-Schrift), Marhurg t 1966).
2) H. Bucher, K. H. Drexhage, M. Fleck, H. Kuhn, D. Möbius, F. P. Schafer, J. Sondermann, W. Sperling, P. Tillmann and J. Wiegand, Mol. Cryst. 2(1967)199.
3) M. Fleck, Weitwinkelinterferenz und Multipolcharakter der Lumineszenz organischer
Farbstoffe (Dissertation). Marhurg (1969).
Discussion on paper 12
Que.vtion 1: W. Gebhardt
I wonder how you prepare the mirror and how you establish a distinct
distance between the surface and the organic molecules?
1.2
INFLUENCE OF A DIELECTRIC INTERFACE ON FLUORESCENCE DECAY TIME
701
Answer: K. H. Drexhage
The metal mirror is evaporated in vacuum. On top of the mirror a certain
number of fatty acid layers are deposited using the technique founded by
Langmuir and Blodgett. Finally a monomolecular layer of a fluorescent dye
is deposited by means of the same technique.
Question 2. G. F. J. Garlick
I wonder if you are aware of some much earlier work by Selenyi, and I
think, some later work by Freed and Weissman in which your effect was
studied in thin acetate films containing dispersed fluorescent molecules. The
study of angular dependence of polarization of the emission was used to
distinguish the nature of the oscillators involved.
Answer: K. H. Drexhage
I am grateful for your comment. In fact, Selenyi’s work has stimulated
us to investigate the angular distribution of fluorescence with the much
more sensitive monolayer technique.
Question 3: W. B. Fowler
For simple systems the absorption cross sections and the reciprocal decay
time are related by the Einstein relation. Does an infinite decay time imply
a zero absorption cross section?
Answer.’ K. H. Drexhage
The Einstein relation holds for molecules in free space. One can derive
a corresponding relationship for molecules in front of a mirror.